摘要
正整数n的分拆是指将正整数n表示成一个或多个正整数的无序和,设O(n,m)表示将正整数n分拆成m个奇数之和的分拆数;e(n,m)表示将正整数n分拆成m个偶数之和的分拆数.本文用初等方法给出了将O(n,m),e(n,m)分别化为有限个O(n,2),e(n,2)的和的计算公式,进而达到计算O(n,m),e(n,m)的值.同时,还讨论了将正整数n分拆成互不相同的奇数或偶数的分拆数的相应的递推计算方法.
A partition of positive integer n is representation of n as unordered sum of one or more positive integers. Let O（n, m） be the number of unordered partitions of an integer n into m odd positive integers. And let e（n, rn） be the number of unordered partitions of a positive integer n into m even parts. In this paper, we show the counting formula by primary method to convert O（n, m） ande（n, re）with finite O（n, 2） and e（n, 2）, respectively. Thus we could calculate the value of O（n, m） and e（n, m）. And we also discussed a counting method for the number of partition with distinct odd and even part, respectively.
出处
《纯粹数学与应用数学》
CSCD
北大核心
2008年第3期525-528,共4页
Pure and Applied Mathematics
基金
甘肃省教育厅科研项目(0709-03)
甘肃省高等学校研究生导师科研项目(0809-04)
关键词
正整数的分拆
分拆数
奇分拆
偶分拆
互不相同的分拆
partition of positive integer, partition number, partition with odd part, partition with even part, partition with distinct part
